Elucidating Three-Dimensional Coherent Structures in a Multi-Stream Jet

TL;DR

This study addresses 3D coherent structures in a realistic three-stream rectangular jet by combining large-eddy simulations with data-driven (SPOD, BIS) and operator-based (triglobal resolvent) analyses. It uncovers two distinct dynamical regimes: broadband, strongly 3D low-frequency structures in the upper and lower shear layers (USL/LSL) and a tonal, predominantly 2D Kelvin–Helmholtz instability in the splitter-plate shear layer (SPSL) at $St = 3.225$. Bispectral analysis reveals nonlinear triadic energy transfer within USL/LSL at low frequencies and energy exchange from the tonal SPSL frequency to its harmonics and mean flow, indicating cross-layer coupling. Triglobal resolvent analysis shows low-frequency amplification with corner-driven forcing that sustains 3D structures and axis-switching, while wavemaker analysis highlights self-sustained corner vortex dynamics as a potent control target. These findings inform strategies to reduce both broadband and tonal jet noise in complex, non-axisymmetric geometries, with implications for propulsion and aeroacoustic design.

Abstract

Nominal two-dimensional (2D) shear layers have been studied extensively, and their principal dynamics are well understood. In practical configurations, however, the behavior of such shear layers is affected by proximal surfaces. In this study, we investigate three-dimensional (3D) coherent structures developing downstream of a relatively thick splitter plate in a realistic nozzle featuring sidewalls, an upper boundary formed by a single expansion ramp, and a lower boundary defined by a protruding deck. As a result, in addition to the primary splitter plate shear layer (SPSL) arising from mixing between the core and bypass streams, the flow contains upper (USL) and lower (LSL) shear layers with the ambient. Large-eddy simulation data are analyzed to characterize the unsteady flow dynamics, while the mean flow provides insight into the underlying amplification mechanisms. Spectral proper orthogonal decomposition reveals a clear separation of broadband and tonal dynamics across frequency bands. The broadband low-frequency modes are highly 3D and originate in the USL and LSL. In contrast, tonal high-frequency content is associated with a 2D instability in the SPSL. Both the broadband and tonal signatures also appear in the nonlinear energy transfer mechanisms. Triglobal resolvent analysis further clarifies the amplification mechanisms within the USL and LSL. Low-frequency response modes are excited by forcing localized near the nozzle geometry and are governed by 3D Kelvin-Helmholtz dynamics. The low-frequency streamwise vortices generated at the nozzle corners drive the axis-switching behavior characteristic of rectangular jets. Wavemaker analysis further demonstrates that these corner vortices are part of self-sustaining low-frequency dynamics.

Figures (13)

• Figure 1: Three-stream turbofan configuration based on the Air Force Research Laboratory (AFRL) design simmons2009. The figure shows an isometric cross-section of the nozzle layout, with the core stream (Mach 1.6) marked in red and the third bypass stream (Mach 1) marked in blue. SERN: Single-sided Expansion Ramp Nozzle.
• Figure 2: (a) Normalized time-averaged streamwise velocity ($\overline{u}/U_{\text{ref}}$) shows three main shear layers, splitter plate shear layer (SPSL), upper shear layer (USL), and lower shear layer (LSL), in the flowfield for nozzle center plane ($z=0$). Iso-surface at level of $\overline{u}/U_{\text{ref}} = 0.4$. (b) Power spectrum density (PSD) of $u$ velocity at the probe located in the SPSL region. (c) Instantaneous pressure fluctuation ($P'/P_{\text{ref}}$) (blue, red) $\in$ [-0.1, 0.1]. (d) Schematic of 3D domain utilized to compute spectral analysis (not to scale).
• Figure 3: The leading five SPOD eigenvalue spectra for (a) upper shear layer (USL), (b) lower shear layer (LSL), and (c) splitter plate shear layer (SPSL). The blue dot-dashed line denotes the leading eigenvalue computed for the entire half-domain in each plot. The dashed orange line indicates the $-5/3$ power law of the energy spectrum. At each frequency, decreasing eigenvalues are shown in lighter shades, i.e., $\lambda_1 \geq \lambda_2 \dots \geq \lambda_5$.
• Figure 4: The leading three SPOD modes for the half-domain case. (a-c) $St = 0.4275$, (d-f) $0.622$, (g-i) $1$, and (j-l) 3.225. Iso-surface of the real component of $u$-velocity is shown. (blue, red) = [-0.3, 0.3].
• Figure 5: Normalized mode bispectrum $\lambda_b = \lambda_1/| \lambda_1|_{\text{max}}$ for the different cases: (a) half-domain, (b) upper shear layer (USL), (c) lower shear layer (LSL), and (d) splitter plate shear layer (SPSL). The constant frequency $St = 3.225$ and $6.45$ are marked by $--$ and $\dots$ lines, respectively. The circles I-VI indicate the dominant triad interactions. (e) Energy cascade in the SPSL regions for the triads highlighted in the circles. Marron solid and blue dashed arrows show the difference and sum interactions. The double-lined arrow presents the energy cascade from the mean flow.